Working Memory Requirements for Problem Solving in Advanced School Mathematics

Abstract

The current study focused on the interplay between general reasoning abilities, working memory functions and math achievement in order to investigate the role of working memory in advanced school mathematics. Based on mathematics test scores and scores on a measure of general reasoning ability (three subtests from the Kognitiver Fähigkeits-Test (KFT), Heller & Perleth, 2000), a sample comprising high-achieving, over-achieving and under-achieving students at advanced placement schools in Switzerland (Swiss Gymnasium) was chosen (N = 120, Mage = 16.3 years). All study participants underwent a working memory test battery arranged by von Bastian and Oberauer (2013), which contains nine different tests targeting all facets of working memory described by the facet model (Oberauer, Süß, Schulze, Wilhelm, & Wittmann, 2000; Oberauer, Süß, Wilhelm, & Wittman, 2003; Süß, Oberauer, Wittmann, Wilhelm, & Schulze, 2002). In addition, they completed a questionnaire on mathematical self-concept and interest in mathematics (the majority of the questionnaire items was utilised in PISA 2000, the items were taken from Gaspard et al., 2015, 2018; Mang et al., 2018; Trautwein, Lüdtke, Marsh, Köller, & Baumert, 2006). Furthermore, two mathematics tests were administered to the study participants, namely a speed test aiming at the knowledge representations of the students and a power test covering mathematical problem solving tasks. For the data analysis, group comparisons between the different groups of students and within the group of high-achievers were carried out. The findings regarding the group comparison between highachieving and over-achieving students suggested that different factors, such as knowledge structures, mathematical self-concept and interest in mathematics could play a role in explaining over-achievement in mathematics. The results related to the group comparison between high-achievers and underachievers identified a poorer mathematical self-concept and a lower performance of the working memory function Storage-Processing as potential root causes of under-achievement in mathematics. Moreover, they showed that in the sample of the current study, under-achievement in mathematics cannot be ascribed to a scarce interest in mathematics. Within the group of high-achievers, the motivational variables of mathematical self-concept and interest in mathematics seemed to be relevant for discriminating between the subgroup of high-achievers with top scores in the Mathematics Power Test and the subgroup of high-achievers with lower scores in the Mathematics Power Test.